Title: 3.1Discovery of the X Ray and the Electron
1CHAPTER 3The Experimental Basis of Quantum Theory
- 3.1 Discovery of the X Ray and the Electron
- 3.2 Determination of Electron Charge
- 3.3 Line Spectra
- 3.4 Quantization
- 3.5 Blackbody Radiation
- 3.6 Photoelectric Effect
- 3.7 X-Ray Production
- 3.8 Compton Effect
- 3.9 Pair Production and Annihilation
As far as I can see, our ideas are not in
contradiction to the properties of the
photoelectric effect observed by Mr. Lenard. -
Max Planck, 1905
23.1 Discovery of the X Ray and the Electron
- X rays were discovered by Conrad Wilhelm Röntgen
in 1895. - Observed x rays emitted by cathode rays
bombarding glass. - Electrons were discovered by J. J. Thomson in
1897. - Observed that cathode rays were charged
particles.
3Cathode Ray Experiments
- In the 1890s scientists and engineers were
familiar with cathode rays. These rays were
generated from one of the metal plates in an
evacuated tube across which a large electric
potential had been established. - It was surmised that cathode rays had something
to do with atoms. - It was known that cathode rays could penetrate
matter and were deflected by magnetic and
electric fields.
4Observation of X Rays
- Wilhelm Röntgen studied the effects of cathode
rays passing through various materials. He
noticed that a phosphorescent screen near the
tube glowed during some of these experiments.
These rays were unaffected by magnetic fields and
penetrated materials more than cathode rays. - He called them x rays and deduced that they were
produced by the cathode rays bombarding the glass
walls of his vacuum tube.
5Röntgens X Ray Tube
- Röntgen constructed an x-ray tube by allowing
cathode rays to impact the glass wall of the tube
and produced x rays. He used x rays to image the
bones of a hand on a phosphorescent screen.
6Apparatus of Thomsons Cathode-Ray Experiment
- Thomson used an evacuated cathode-ray tube to
show that the cathode rays were negatively
charged particles (electrons) by deflecting them
in electric and magnetic fields.
7Thomsons Experiment
- Thomsons method of measuring the ratio of the
electrons charge to mass was to send electrons
through a region containing a magnetic field
perpendicular to an electric field.
8Calculation of e/m
- An electron moving through the electric field is
accelerated by a force - Electron angle of deflection
- The magnetic field deflects the electron against
the electric field force. - The magnetic field is adjusted until the net
force is zero. - Charge to mass ratio
93.2 Determination of Electron Charge
- Millikan oil drop experiment
10Calculation of the oil drop charge
- Used an electric field and gravity to suspend a
charged oil drop. - Mass is determined from Stokess relationship of
the terminal velocity to the radius and density. - Magnitude of the charge on the oil drop.
- Thousands of experiments showed that there is a
basic quantized electron charge.
C
113.3 Line Spectra
- Chemical elements were observed to produce unique
wavelengths of light when burned or excited in an
electrical discharge. - Emitted light is passed through a diffraction
grating with thousands of lines per ruling and
diffracted according to its wavelength ? by the
equation - where d is the distance of line separation and n
is an integer called the order number.
12Optical Spectrometer
- Diffraction creates a line spectrum pattern of
light bands and dark areas on the screen. - The line spectrum serves as a fingerprint of the
gas that allows for unique identification of
chemical elements and material composition.
13Balmer Series
- In 1885, Johann Balmer found an empirical formula
for wavelength of the visible hydrogen line
spectra in nm -
-
nm (where k 3,4,5)
14Rydberg Equation
- As more scientists discovered emission lines at
infrared and ultraviolet wavelengths, the Balmer
series equation was extended to the Rydberg
equation
153.4 Quantization
- Current theories predict that charges are
quantized in units (called quarks) of e/3 and
2e/3, but quarks are not directly observed
experimentally. The charges of particles that
have been directly observed are quantized in
units of e. - The measured atomic weights are not
continuousthey have only discrete values, which
are close to integral multiples of a unit mass.
163.5 Blackbody Radiation
- When matter is heated, it emits radiation.
- A blackbody is a cavity in a material that only
emits thermal radiation. Incoming radiation is
absorbed in the cavity.
- Blackbody radiation is theoretically interesting
because the radiation properties of the
blackbody are independent of the particular
material. Physicists can study the properties of
intensity versus wavelength at fixed temperatures.
17Wiens Displacement Law
- The intensity (?, T) is the total power
radiated per unit area per unit wavelength at a
given temperature. - Wiens displacement law The maximum of the
distribution shifts to smaller wavelengths as the
temperature is increased.
18Stefan-Boltzmann Law
- The total power radiated increases with the
temperature - This is known as the Stefan-Boltzmann law, with
the constant s experimentally measured to be
5.6705 10-8 W / (m2 K4). - The emissivity ? (? 1 for an idealized
blackbody) is simply the ratio of the emissive
power of an object to that of an ideal blackbody
and is always less than 1.
19Rayleigh-Jeans Formula
- Lord Rayleigh (John Strutt) and James Jeans used
the classical theories of electromagnetism and
thermodynamics to show that the blackbody
spectral distribution should be - It approaches the data at longer wavelengths, but
it deviates badly at short wavelengths. This
problem for small wavelengths became known as
the ultraviolet catastrophe and was one of the
outstanding exceptions that classical physics
could not explain.
exp(x) 1 x for very small x, i.e. when h ? 0,
d. h. classical physics (also for f small and T
large)
20Plancks Radiation Law
- Planck assumed that the radiation in the cavity
was emitted (and absorbed) by some sort of
oscillators that were contained in the walls.
He used Boltzmans statistical methods to arrive
at the following formula that fit the blackbody
radiation data. - Planck made two modifications to the classical
theory - The oscillators (of electromagnetic origin) can
only have certain discrete energies determined by
En nhf, where n is an integer, f is the
frequency, and h is called Plancks constant. h
6.6261 10-34 Js. - The oscillators can absorb or emit energy in
discrete multiples of the fundamental quantum of
energy given by
Plancks radiation law
213.6 Photoelectric Effect
- Methods of electron emission
- Thermionic emission Application of heat allows
electrons to gain enough energy to escape. - Secondary emission The electron gains enough
energy by transfer from another high-speed
particle that strikes the material from outside. - Field emission A strong external electric field
pulls the electron out of the material. - Photoelectric effect Incident light
(electromagnetic radiation) shining on the
material transfers energy to the electrons,
allowing them to escape.
Electromagnetic radiation interacts with
electrons within metals and gives the electrons
increased kinetic energy. Light can give
electrons enough extra kinetic energy to allow
them to escape. We call the ejected electrons
photoelectrons.
22Experimental Setup
23Experimental Results
- The kinetic energies of the photoelectrons are
independent of the light intensity. - The maximum kinetic energy of the photoelectrons,
for a given emitting material, depends only on
the frequency of the light. - The smaller the work function f of the emitter
material, the smaller is the threshold frequency
of the light that can eject photoelectrons. - When the photoelectrons are produced, however,
their number is proportional to the intensity of
light. - The photoelectrons are emitted almost instantly
following illumination of the photocathode,
independent of the intensity of the light.
24Experimental Results
25Classical Interpretation
- Classical theory predicts that the total amount
of energy in a light wave increases as the light
intensity increases. - The maximum kinetic energy of the photoelectrons
depends on the value of the light frequency f and
not on the intensity. - The existence of a threshold frequency is
completely inexplicable in classical theory. - Classical theory would predict that for extremely
low light intensities, a long time would elapse
before any one electron could obtain sufficient
energy to escape. We observe, however, that the
photoelectrons are ejected almost immediately.
26Einsteins Theory
- Einstein suggested that the electromagnetic
radiation field is quantized into particles
called photons. Each photon has the energy
quantum - where f is the frequency of the light and h is
Plancks constant. - The photon travels at the speed of light in a
vacuum, and its wavelength is given by
27Einsteins Theory
- Conservation of energy yields
- where is the work function of the metal.
- Explicitly the energy is
- The retarding potentials measured in the
photoelectric effect are the opposing potentials
needed to stop the most energetic electrons.
28Quantum Interpretation
- The kinetic energy of the electron does not
depend on the light intensity at all, but only on
the light frequency and the work function of the
material. - Einstein in 1905 predicted that the stopping
potential was linearly proportional to the light
frequency, with a slope h, the same constant
found by Planck. - From this, Einstein concluded that light is a
particle with energy
293.7 X-Ray Production
- An energetic electron passing through matter will
radiate photons and lose kinetic energy which is
called bremsstrahlung, from the German word for
braking radiation. Since linear momentum must
be conserved, the nucleus absorbs very little
energy, and it is ignored. The final energy of
the electron is determined from the conservation
of energy to be - An electron that loses a large amount of energy
will produce an X-ray photon. Current passing
through a filament produces copious numbers of
electrons by thermionic emission. These electrons
are focused by the cathode structure into a beam
and are accelerated by potential differences of
thousands of volts until they impinge on a metal
anode surface, producing x rays by bremsstrahlung
as they stop in the anode material.
30Inverse Photoelectric Effect.
- Conservation of energy requires that the electron
kinetic energy equal the maximum photon energy
where we neglect the work function because it is
normally so small compared to the potential
energy of the electron. This yields the
Duane-Hunt limit which was first found
experimentally. The photon wavelength depends
only on the accelerating voltage and is the same
for all targets.
313.8 Compton Effect
- When a photon enters matter, it is likely to
interact with one of the atomic electrons. The
photon is scattered from only one electron,
rather than from all the electrons in the
material, and the laws of conservation of energy
and momentum apply as in any elastic collision
between two particles. The momentum of a particle
moving at the speed of light is - The electron energy can be written as
- This yields the change in wavelength of the
scattered photon which is known as the Compton
effect
323.9 Pair Production and Annihilation
- If a photon can create an electron, it must also
create a positive charge to balance charge
conservation. - In 1932, C. D. Anderson observed a positively
charged electron (e) in cosmic radiation. This
particle, called a positron, had been predicted
to exist several years earlier by P. A. M. Dirac. - A photons energy can be converted entirely into
an electron and a positron in a process called
pair production.
33Pair Production in Empty Space
- Conservation of energy for pair production in
empty space is - Considering momentum conservation yields
- This energy exchange has the maximum value
- Recall that the total energy for a particle can
be written as - However this yields a contradiction
- and hence the conversion of energy in empty
space is an impossible situation.
34Pair Production in Matter
- Since the relations
and contradict each other, a
photon can not produce an electron and a positron
in empty space. - In the presence of matter, the nucleus absorbs
some energy and momentum. - The photon energy required for pair production in
the presence of matter is
35Pair Annihilation
- A positron passing through matter will likely
annihilate with an electron. A positron is drawn
to an electron by their mutual electric
attraction, and the electron and positron then
form an atomlike configuration called
positronium. - Pair annihilation in empty space will produce two
photons to conserve momentum. Annihilation near a
nucleus can result in a single photon. - Conservation of energy
- Conservation of momentum
- The two photons will be almost identical, so that
- The two photons from positronium annihilation
will move in opposite directions with an energy